Linear, time-invariant (LTI) systems can be said to perform only four
operations on a signal: copying, scaling, delaying, and adding. As a
result, each output is always a
linear combination of delayed copies of the input signal(s).
(A linear combination is simply a weighted sum, as discussed in
§5.6.) In any linear
combination of delayed copies of a complex sinusoid

where is a weighting factor, is the th delay, and

is a complex sinusoid, the ``carrier term''
can be ``factored out'' of the linear combination:

Since every signal can be expressed as a linear combination of complex
sinusoids, this analysis can be applied to any signal by expanding the
signal into its weighted sum of complex sinusoids (i.e., by expressing
it as an inverse Fourier transform).